Jonkershoek eddy covariance

model{

  #### Data Model
  for(t in 1:n){
    y[t] ~ dnorm(x[t],tau_obs)
  }

  #### Process Model
  for(t in 2:n){
    x[t]~dnorm(x[t-1],tau_add)
  }

  #### Priors
  x[1] ~ dnorm(x_ic,tau_ic)
  tau_obs ~ dgamma(a_obs,r_obs)
  tau_add ~ dgamma(a_add,r_add)
}

model{

  #### Data Model
  for(t in 1:n){
    y[t] ~ dnorm(x[t],tau_obs)
  }

  #### Process Model
  for(t in 2:n){
    x[t] <- rho * x[t-1] + b1 * light[t] + b2*temperature[t] + alpha[t-1]
  }

  #### Priors
  x[1] ~ dnorm(0,0.1)  # initial condition
  tau_obs ~ dgamma(1,1)  # observation error
  for (i in 1:(n-1)) {alpha[i] ~ dnorm(0,tau_add)}
  tau_add ~ dgamma(1,1) # process error
  rho ~ dunif(-1,1)  # autocorrelation
  b1 ~ dnorm(0,0.1) # coefficient for light
  b2 ~ dnorm(0,0.1)  # coefficient for temperature
}
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